U.S. patent number 4,302,813 [Application Number 06/013,820] was granted by the patent office on 1981-11-24 for method of controlling operation of rotary machines by diagnosing abnormal conditions.
This patent grant is currently assigned to Hitachi, Ltd.. Invention is credited to Shigeyoshi Kawano, Nobuo Kurihara, Mitsuyo Nishikawa.
United States Patent |
4,302,813 |
Kurihara , et al. |
November 24, 1981 |
Method of controlling operation of rotary machines by diagnosing
abnormal conditions
Abstract
The present invention relates to a method of controlling the
operation of large rotary machines such as steam turbines and
generators in a thermal power plant or nuclear power plant. More
specifically, the invention relates to a method of controlling such
operation as increasing or decreasing the speed of the rotary
machines or stopping the operation of the rotary machines, by
detecting vibration at the time of starting the operation or during
the steady-speed operation, by analyzing the detected vibration
signals to determine whether the operation is in normal condition
or abnormal condition, and by detecting or forecasting the cause in
case the operation is in abnormal condition.
Inventors: |
Kurihara; Nobuo (Ibaraki,
JP), Nishikawa; Mitsuyo (Ibaraki, JP),
Kawano; Shigeyoshi (Ibaraki, JP) |
Assignee: |
Hitachi, Ltd. (Tokyo,
JP)
|
Family
ID: |
11972959 |
Appl.
No.: |
06/013,820 |
Filed: |
February 22, 1979 |
Foreign Application Priority Data
|
|
|
|
|
Feb 22, 1978 [JP] |
|
|
53-18486 |
|
Current U.S.
Class: |
702/56; 73/462;
73/579; 73/660 |
Current CPC
Class: |
F01D
19/00 (20130101); G01H 1/003 (20130101); F01D
21/14 (20130101) |
Current International
Class: |
F01D
21/00 (20060101); F01D 19/00 (20060101); F01D
21/14 (20060101); G01H 1/00 (20060101); G06F
015/46 (); G01N 029/00 () |
Field of
Search: |
;364/494,508
;73/462,579,593 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Wise; Edward J.
Attorney, Agent or Firm: Craig and Antonelli
Claims
What is claimed is:
1. A method of controlling a build-up speed of a rotary machine
with a vibration-monitoring system comprising a
vibration-responsive means preferably containing at least one
vibration transducer mounted on a bearing, a running speed detector
which transduces signals responding to the rotary machine speed, a
diagnosing device with a frequency analyzer which analyzes a
vibration signal from the vibration transducer, and a speed
regulator which controls the speed of the rotary machine responding
to demand signals as a result of the vibration frequency analysis,
comprising:
a first step of discriminating in which speed region a running
speed of the rotary machine lies among a plurality of predetermined
speed regions which are obtained by dividing the speed range, from
start up to rated speed of the rotary machine, into critical
speeds,
a second step of calculating harmonic components of a frequency
spectrum which are predetermined in the respective divided speed
regions,
a third step of discriminating as to which one of a plurality of
predetermined operating patterns corresponds to said calculated
harmonic components of the frequency spectrum, which patterns
include a speed raising region and a speed lowering region, which
are closely related with components of rotation frequency, and
a fourth step of performing a predetermined speed control operation
of the rotary machine depending on the discrimination result in
said third step.
2. A method according to claim 1, wherein a build-up speed is
controlled while monitoring the harmonic components of frequency
corresponding to one-half of the rotation frequency of said rotary
machine, and is controlled in accordance with said patterns which
have been determined beforehand in response to the harmonic
components of said rotation frequency.
3. A method according to claim 1, wherein a build-up speed is
controlled with monitoring the harmonic components corresponding to
one-third of the rotation frequency in the running speed of said
rotary machines, and is controlled in accordance with said patterns
which have been determined beforehand in response to the harmonic
components of said rotation frequency.
4. A method according to claim 1, wherein a build-up speed is
controlled with monitoring the second harmonic of the fundamental
frequency in the running speed of said rotary machines, and is
controlled in accordance with said patterns which have been
determined beforehand in response to the harmonic components of
said rotation frequency.
5. A method according to claim 1, wherein a build-up speed is
controlled with monitoring the components of a specific frequency
corresponding to a critical speed of the rotary machines, and is
controlled in accordance with the patterns which have been
determined beforehand in response to the components of said
specific frequency.
6. A method according to claim 1, wherein the build-up speed
control operation patterns include a speed-raising region, a
speed-holding region, a speed-lowering region in which the running
speed is lowered to a region smaller than a critical speed closest
to the running speed in said holding region, and a tripping region,
responsive to the harmonic components of vibration signals, and the
build-up speed is controlled in accordance with said speed control
operation patterns.
7. A method according to claim 1, wherein the vibration signals are
analyzed, and the harmonic components of the rotation frequency,
the harmonic components of a frequency corresponding to one-half of
the rotation frequency, the harmonic components of a frequency
corresponding to one-third of the rotation frequency, the second
harmonic of the fundamental frequency in the running speed, and the
components of a specific frequency corresponding to the critical
speed of the rotary machines are simultaneously monitored, and the
build-up speed is controlled according to the operation pattern of
the highest level among their harmonic components.
8. A method according to claim 1, wherein the harmonic components
in a region corresponding to (1/2.+-.r)(wherein r is a natural
number of 1, 2, . . . ) of the components of the rotation frequency
are monitored.
9. A method according to claim 1, wherein the harmonic components
in a region corresponding to (1/3.+-.r)(wherein r is a natural
number of 1, 2, . . . ) of the components of the rotation frequency
are monitored.
10. A method according to claim 1, wherein the harmonic components
in a region corresponding to (2.+-.r)(wherein r is a natural number
of 1, 2, . . . ) of the components of the rotation frequency are
monitored.
11. A method according to claim 1, wherein the harmonic components
in a region in the vicinity r of a specific frequency to the rotary
machine are monitored.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method of controlling the
operation of large rotary machines such as steam turbines or
generators while monitoring the vibrating state during the
operation and especially at the time of starting.
The problem of vibration of rotary members occupies a great
proportion of the maintenance time in operating thermal power
stations, and the investigation of the causes and the
countermeasures required to correctly grasp the situations require
a detailed technical study. Further, the distance between the
centers of the bearings, the weight of the rotors and the number of
wheel chambers are on the increase accompanying the recent trend
toward increased capacities of steam turbines, thereby causing the
problem of vibration to become more complicated.
In regard to the control of power systems, on the other hand, it is
also a modern trend to operate the thermal power plant to adjust
the intermediate load while the base loads are being carried out by
the nuclear power plant. The conventional weekly adjustment of load
is now shifting toward the adjustment of load in daytime.
Therefore, the machines of medium capacities in thermal stations
are often stopped during such time zones as midnight in which the
demand for power is small. In starting and stopping the operation
of the plant, the abnormal condition tends to develop as compared
with the case of steady-state operation. In starting the turbines
particularly, the abnormal vibration tends to develop which is
caused by the thermal unbalance.
In operating the steam turbines or generators, the operation staffs
must pay their most careful attention at the time of starting the
machines; the development of abnormal vibration during the starting
presents a serious problem. Lack of proper treatment or the timing
may result in a serious accident, particularly with the steam
turbines which revolve at high speeds.
Even during the steady-state operation, any abnormal condition must
be detected as early as possible and proper treatment must be
effected in quickly so that it will not develop into a serious
accident. The vibration during the steady-state operation also
presents the same problem as that at the time of starting the
operation.
According to the present invention, the normal or abnormal
conditions of the rotary machines are monitored and discriminated,
i.e., the states of the vibration signals are detected by vibration
detectors which are installed, for example, on the bearings, and
are monitored and discriminated, to thereby control the
operation.
The present invention attained under such circumstances analyzes
the detected vibration signals and stably controls the operation
while locating the cause, in order to prevent any serious
accident.
2. Description of the Prior Art
In starting the operation of a steam turbine, an apparatus for
controlling the turbine speed operates a main steam valve or a
by-pass valve responsive to a desired running speed of the turbine
and a desired variation factor in running speed, so that the
running speed is gradually increased.
In case vibration has developed during the speed-up, however, any
one of the following three methods has so far been employed
depending upon the amplitude of the vibration signals. The first
method is to stop the speed-rising control by the speed-control
apparatus and to switch the operation into a manual control so that
the operation is controlled depending upon the discretion by the
operating staffs. The second method is to maintain the running
speed at a speed at which the vibration had developed, and not to
effect the speed-rising control. The third method is to stop the
turbine.
According to the first method, however, the control which is
switched to the manual operation depends entirely upon the
discretion of the operation staffs. Therefore, the persons skilled
in this field of art are required. Further, the control of
operation differs depending upon the individual staffs, and is not
desirable.
According to the second method, there arises a problem of specific
vibrating frequency during the running of rotary machines.
Therefore, it is not necessarily desirable to maintain the running
speed of the rotary machines at a speed at which the vibration is
developed.
It has been known that the vibration increases in a critical speed
region determined by the specific vibrating frequency of rotary
machines consisting of turbines and generators directly coupled to
the turbines. Accordingly, to maintain the running speed at a
predetermined value as done by the abovementioned second method
rather presents very dangerous conditions.
With the third method, on the other hand, the rotary members can be
safely handled. The third method, however, is likely to effect
unnecessary tripping. The vibration is caused by a variety of
factors such as thermal unbalance, mechanical unbalance, state of a
lubricating oil and running speed, and it is difficult to forecast
the normal and abnormal conditions. Depending upon the cases,
therefore, the vibration can be converged into a safe vibration
region by maintaining the running speed of the rotary machines at a
given value as accomplished by the abovementioned second method.
Therefore, frequent use of the third method often results in
unnecessary tripping. Conversely, if the standard for discretion is
loosened to avoid the tripping, proper treatment may not often be
effected under abnormal conditions.
What is important here is to determined whether it is safe to
maintain the running speed thereby avoiding the tripping.
Therefore, desirable effects will not be obtained unless it is
determined in which speed region the rotary machine is rotating
without maintaining the running speed in a dangerous region, and
unless it is diagnosed what phenomenon is appearing as a cause of
vibration.
Among the aforementioned causes of vibration, a countermeasure has
been attempted in regard to the mechanical unbalance in order to
minimize the development of vibration.
An example can be found, for instance, in J. W. Lund, J. Tonnesen:
"Analysis and Experiments on Multi-Plane Balancing of a Flexible
Rotor," ASME Paper No. 71-Vibr-74 (ASME Vibrations Conference,
Tront, Canada, Sept. 8-10, 1971). This literature mentions to
attain balance by detecting vibration in several places of a rotary
machine, detecting the rotating speed, and calculating a correction
weight by utilizing the method of least square. As for the method
of measuring vibration, the literature schematically diagramatizes
the instrumentation in FIG. 4, and gives the related description is
a paragraph of "Instrumentation" (pp. 3 to 4).
Further, A. Clapis et al "Early Diagnosis of Dynamic Unbalances and
of Misalignments in Large Turbogenerators", Energy Nuclear, Vol.
23/n. 5/maggio, 1976, pp. 271 to 277, discloses the measurement of
dynamic unbalance and misalignment of axis of large turbine
generators to apply it as an early diagnosis to cope with the
troubles. This literature mentions two measuring methods,
processing of signals for monitoring and early diagnosis, and
relation between the amplitude and the phase caused by the
unbalanced rotary members with reference to the rotating speed.
Particularly, FIG. 2 of this literature shows a state for mounting
the proximity transducers, and FIG. 3 shows a block diagram for
processing the signals. According to this literature, the signals
from the proximitors are subjected to the signal conversion through
a predetermined BP filter. The literature, further, mentions to
convert the vibration-phase signals or vibration signals of root
mean square values into d-c components to record them.
Thus, according to most of the conventional arts, the vibration
signals are smoothed and treated in the form of d-c components.
According to such methods for treating the signals, however, a
variety of factors are all diagnosed as a whole, making it
difficult to effect fine diagnosis.
Further, F. H. Barratt et al., "ACTUS, An Automatically Controlled
Turbine Run-up System", AEI Engineering, September/October, 1962,
pp. 255-258, discloses a method that is practically applied to the
operation for starting turbines.
This literature discusses the apparatus ACTUS that was developed by
AEI, and mentions the speed-raising operation of turbines in a
paragraph of "Problems of starting large steam turbine" on pages
255 to 256. This literature clearly mentions to raise the speed of
the turbines while monitoring the misalignment of axis, vibration
and temperature difference between the steam and the metals, which
are out of the ordinarily specified ranges, as well as to maintain
the speed no matter how fast or slowly the turbines may be running.
This, however, is a method of controlling the running speed to a
predetermined value under abnormal conditions as mentioned earlier,
and is not necessarily advantageous.
In the foregoing were mentioned conventional arts for controlling
the operation based on the results of the diagnosis of abnormal
conditions, by way of (1) switching the controlling operation into
manual controlling operation, (2) maintaining the running speed,
and (3) tripping. The signals have been processed by way of
smoothing, i.e., signals of average values or d-c signals have been
brought into diagnosis.
The signals can be easily processed only if the signals of average
values are employed. Thus the diagnosis is not possible unless the
signals are converted into those of average values. That is, in
case some particular frequency components are increased and other
particular frequency components are decreased, the resulting
decision will be that the state is not changed unless the average
value is changed.
In practice, however, even when the average value is not changed,
the increase of some particular frequency components will have to
be often regarded seriously. Though the increases of such
particular frequency components may not directly be related to the
abnormal conditions, we know through experience that it is the
beginning of abnormal conditions.
Consequently, when the vibration signals are diagnosed in the form
of average values of the whole frequency components, it is
difficult to correctly and faithfully diagnose the symptoms. The
present invention is based on this fact, and makes it possible to
safely control the operation of the turbogenerators, particularly
at the time of starting the operation, based on a proper diagnosis
which meets the practical demands.
SUMMARY OF THE INVENTION
The principal object of the present invention is to monitor the
predetermined vibration frequency components and to diagnose the
operating state of rotary members, particularly, the
turbogenerators.
It is also an object of the present invention to provide a method
of controlling the speed of turbogenerators by monitoring at least
one predetermined vibration frequency component in a plurality of
predetermined operating speed regions at the time of starting the
operation, thereby to diagnose the state of operation.
Another object of the present invention is to so control the
operation as to increase the running speed, decrease the running
speed or hold the speed, by monitoring particular frequency
components to forecast and diagnose the abnormal conditions,
particularly at the time of the starting operation.
A feature of the present invention is to diagnose the state of the
rotary members by monitoring at least one vibration frequency
component having a predetermined relation with respect to the
running speed of the turbogenerator, among the detected vibration
signals.
Another feature of the present invention is to monitor and diagnose
the state of the turbine and generator from correlations among a
plurality of frequency components having predetermined relations
with respect to the running speed, among the detected vibration
signals.
A further feature of the present invention is to control the
operation of a rotary member by diagnosing the state of frequency
components at the running speed and the state of frequency
components having predetermined relations in the vicinities of
critical speed regions determined from the specific vibrations of
the rotary members existing from the start of the operation to a
rated running speed of the rotary members.
Still another feature of the present invention is the control of
the operation of a rotary member at the time of starting of the
operation by diagnosing the states of the frequency components at a
running speed of the rotary member, components of halved harmonica,
components of odd harmonics and components of doubled
harmonics.
Yet another feature of the present invention is to diagnose the
running state of the turbogenerator by analysing the spectrum of
all frequency components of the detected vibration signals.
A further feature of the present invention is to perform the
operation according to an operation pattern consisting of four
regions, i.e., a region of raising the speed, a region of holding
the operation, a region in which the speed is dropped below a
critical speed closest to the region of holding the operation, and
a region of tripping.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a sketch showing a state in which large turbogenerators
are coupled together;
FIG. 2 is a block diagram showing a state for mounting a vibration
amplitude detector on a bearing and for processing the signals;
FIG. 3 is a block diagram showing a method of analysing the
vibration signals by FHT;
FIG. 4 is a diagram showing vibrating amplitude characteristics,
the abscissa representing the time t, and the ordinate representing
the vibrating amplitude x;
FIG. 5 is a diagram in detail of an A/D converter, an FHT converter
and a band average frequency converter;
FIG. 6 is a flow diagram showing in detail the arithmetic operation
by the FHT converter;
FIG. 7 is a flow diagram showing the case when the arithmetic
operation by the FHT converter of FIG. 6 and a linear conversion
are carried out by a digital computer;
FIG. 8 is a flow diagram of arithmetic operation when the FHT
arithmetic operation of FIG. 6 and the linear conversion are
combined together;
FIG. 9 is a flow diagram of arithmetic operation when the operation
of FIG. 8 is carried out by means of a digital computer;
FIG. 10 is a block diagram when the speed of the turbine is
practically controlled by diagnosing the vibration;
FIG. 11 is a block diagram which is a more concrete representation
of the apparatus for diagnosing the vibration of FIG. 10;
FIG. 12 comprised of 12(a)-12(d) is a diagram showing examples of
signal waveforms at each of the portions of FIG. 11;
Diagram (a) of FIG. 13 shows a relation between a rotating speed
and a vibrating amplitude of a rotary machine, and a sheltered
speed region, and diagram (b) shows a relation between a starting
schedule and the sheltered speed region;
FIG. 14 is a diagram showing an example of the operation pattern
determined by the analyzed frequency components;
Diagrams (A) and (B) of FIG. 15 are flow diagrams for illustrating
the frequency analysis of the vibration signals and the method of
controlling the operation, and diagrams (C), (D) and (E) show
examples of the operation pattern;
Diagram (a) of FIG. 16 shows an example of the vibrating amplitude
by the oil whirl and rubbing with respect to the rotating speed,
diagram (b) shows an example of vibration signals at point a in the
diagram (a), diagram (c) shows an example of vibration signals at a
point b caused by the oil whirl, and diagram (d) shows spectra of
frequency at points a and b in diagram (a); and
FIG. 17 is a diagram showing the starting characteristics of the
present invention in comparison with the conventional art.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
Briefly, the fundamental items for the diagnosis of abnormal
conditions by analyzing frequency components as contemplated by the
present invention will be discussed.
In regard to large rotary machines, especially in regard to
turbogenerators which are constructed in large capacities in recent
years, it is very important to diagnose the abnormal conditions at
an early stage and to take the necessary correctional measures. The
problem here will deal with signals from which the abnormal
conditions may be diagnosed. Below is briefly mentioned the method
of analyzing the vibration signals from the detectors mounted on
the bearings.
FIG. 1 shows an example of a large turbogenerator consisting of a
high-pressure turbine HP, an intermediate-pressure turbine IP, a
low-pressure turbine LP, and a generator that are directly coupled
together. Reference numerals 1 to 6 represent bearings on which are
usually mounted vibration detectors.
FIG. 2 shows an example in which a vibration detector is mounted,
wherein reference numeral 11 denotes a rotary member (shaft), 12 a
vibration detector (transducer), 13 a sample-holding circuit, 14 an
analog-to-digital converter (A/D converter), and reference numeral
15 denotes an FFT (Fast Fourier Transformer). Among the signal
lines, reference numeral 101 represents a vibration amplitude
analog signal, 102 a vibration amplitude digital signal, and
reference numeral 103 denotes a spectrum signal of the whole of the
vibration frequencies. Although FIG. 2 shows a vibration detector
of a contacting type, the vibration detector may of course be of a
non-contacting type provided it detects the vibration of the
machine.
FIG. 2 shows the case of employing an FFT which is suited for the
diagnosis of abnormal conditions of a rotary machine where a
plurality of factors are correlated in a complicated manner. The
reason is because, the features in most cases can be easily
extracted if the time series signals are transformed into frequency
regions. In recent years therefore it has been attempted to utilize
a high-speed Fourier transform in on-line system in performing
factory test, installation adjustment or when trouble develops. For
example, Japanese Patent Laid-Open No. 1411/72 entitled "Apparatus
for processing data by high-speed Fuorier Transform" (filed by IBM
on July 6, 1970, corresponding U.S. patent application Ser. No.
52,332) discloses to make a hardware for a variety of high-speed
Fourier transformation algorithm for calculating isolated Fourier
transforms, among many methods for numerically solving problems
utilizing isolated Fourier transformations. Although the disclosure
of this Laid-Open publication has no relation to the diagnosis of
abnormal conditions of rotary machine, there is a discussion
mentioned concerning the use of an FFT. Reference should be made to
the above publication for the details of the FFT. A brief
discussion of the FFT follows.
As is well known, an isolated Fourier transformation of equation
(1) is operated at a high speed by way of row substitution of a
Fourier matrix F and Good's formula for the resolution into
factors.
Here, the Fourier coefficient a is
where, N represents a number of samples, F Fourier matrix, and X a
time series signal. They can further be given by the equations (2)
and (3)
where T represents transposition, i a frequency or harmonic
frequency, and i, l=0, 1, 2, 3,-(N-1).
The time series signal X.sup.T is given by
which is a time series signal of a vibrating waveform.
A symbol .DELTA.W represents a phase-correcting operator for
performing the analysis at a central point in the sampling point.
##EQU1##
The FFT transformer is now finding widespread applications as it
makes it possible to easily find the spectrum of all frequencies of
time series signals. However, in diagnosing the turbines and
generators in on-line systems, it is necessary to keep the
monitoring at all times irrespective of whether the operation is
under normal or abnormal conditions. To cope with the emergency,
the results of analysis must be directly connected to the analysis
of factors under abnormal conditions.
That is, to employ the FFT algorithm of the conventional art for
diagnosing abnormal conditions while monitoring at all times,
provides the advantage that the spectrum of all frequencies of the
time series signals can be easily found as mentioned in the
foregoing, but presents the below-mentioned defects.
The first defect is that the multiplication of W(=exp (-j2.pi./N))
of the equation (3) must be performed (1/2N)log.sub.2 N times,
(here N represents the number of samples), which is a too great
burden for calculating using a control computer in real time.
The second defect is that although the spectrum of all frequencies
can be obtained, the operating staffs still must determine and
analyze the factors from the distributed contents, which is not
desirable in emergency cases.
As for the first defect, the calculating speed can be
advantageously heightened using an FFT composed of the exclusively
designed hardwares. This, however, requires increased manufacturing
cost as compared with the case of softwares. The utility value,
however, may increase provided the hardware can be cheaply
manufactured.
There is also a method of analysing the frequencies (or correctly,
analysing the sequency) by utilizing the Fast Hadamard Transformer
(hereinafter referred to as FHT) which analyses the time series
input signals with rectangular waves as reference waves. The FHT is
also called a Walsh-Hadamard Transformer (abbreviated as WHT). In
regard to this method of frequency analysis, reference should be
made, for example, to "BIFORE OR Hadamard Transform" by Nasir Ahmed
et al (IEEE Transaction on Audio and Electroacoustics, September
1971, pp. 225 to 234).
FIG. 3 is a block diagram employing the FHT. An FHT analyzer is
denoted by reference numeral 16 and a band average frequency
analyzer is denoted by 17.
An input signal consists of a signal 104 having a sequency
coefficient A obtained by FHT-transforming the time series digital
signals, and a band frequency spectrum signal is found based on a
linear transform coefficient K which has been specified beforehand,
or a band average frequency spectrum signal 105 is obtained based
on an average linear transform coefficient K.multidot.K and K will
be mentioned later in detail.
Below is briefly mentioned the FHT.
The FHT system which processes the time series input signals,
produces a sequency coefficient A which is defined as follows:
where n=log.sub.2 N
sequency coefficient: A.sup.T =[A.sub.0,A.sub.1,A.sub.2,-.
A.sub.N-1 ], where T is transposition, substituted matrix: T
where x denotes a Kronecker product.
diagonal matrix: E.sup.(0) =1 ##EQU2##
Here, the Walsh and Fourier Transfer (hereinafter referred to as
WFT) is a method for transforming the sequency coefficient A into a
Fourier coefficient a in accordance with the equation (7).
Here, the linear transform coefficient K is given by the equation
(8).
As will be obvious from the equation (6), only the addition and the
subtraction need be carried out. Therefore, as compared with the
FFT which performs the multiplication of complex numbers such as of
sine and cosine, the above method is capable of processing the
calculation needing one-tenth or less of the operation time. This
is particularly desirable when the abnormal conditions of the
rotary machines are to be diagnosed in an on-line system. For
instance, this method proves to be particularly preferable in
diagnosing the turbines at the time of starting the operation.
Symbols F and H represent Fourier matrix and Hadamard matrix of the
Nth order. Namely, according to the FHT system, the sequency
coefficient output A can be transformed into a Fourier coefficient
for indicating the frequency components by utilizing a linear
transform coefficient K.
Based on these fundamental items, the present invention is
mentioned below with reference to embodiments.
First, below are mentioned the analysis of the detected vibration
signals and the diagnosis of abnormal conditions.
The present invention is based on the use of the aforementioned
FHT. The present invention, however, is not to find the coefficient
a of all frequencies for materializing the high speed, but is to
find any given band average frequency a in accordance with the
equation (9).
Here, the average linear transform coefficient is, ##EQU3## average
linear transform coefficients K.sub.p which we empirically selected
to cope with abnormal vibration of the rotary machines.
TABLE 1 ______________________________________ Reference for
Example of P Cause of vibration selecting K.sub.p-- --K.sub.p
selected ______________________________________ 1 Misalignment of
Fractional harmonic i = 29, 30, bearings vibration (even 31, 14,
15, order 1/2R) 16 (m.sub.1 = 6) 2 Loosened couplings Fractional
harmonic i = 19, 20, vibration (odd 21, 11, 12, order 1/3R) 13
(m.sub.2 = 6) 3 Self-exicited vi- Critical speed i = 21, 22,
bration caused (Rc) 23 (m.sub.3 = 3) by oil-film characteristics in
the bearings 4 Thermal bending Rotating speed i = 59, 60, caused by
rubbing (R) 61 (m.sub.4 = 3) 5 Unbalance in Doubled harmonics i =
119, rigidity vibration (2R) 120, 121 (m.sub.5 = 3)
______________________________________ Note: R represents
components of running speed, and Rc represents specific
frequency.
Table 1 shows the examples of the average linear transform
coefficients K.sub.p of the turbines and generators which revolve
at high speeds in thermal or nuclear power stations. The causes of
abnormal vibration are roughly divided into five: (1) misalignment
of bearings, (2) loosened couplings, (3) self-excited vibration
caused by the oil-film characteristics in the bearings, (4) thermal
bending caused by rubbing, and (5) unbalance in rigidity. Analysis
of the frequencies of vibrations caused by these factors indicates
that the vibrations have their specific frequency regions. Namely,
it has been found that the frequency components (spectra) develop
in the form of fractional harmonics vibration and doubled harmonics
vibrations depending upon the causes. Consequently, if the
frequency components are found depending upon the fractional
harmonics components and doubled harmonics, it is allowed to know
the degree of causes.
Table 1 shows relations among such causes. It was already mentioned
that the FHT is capable of greatly reducing the processing time as
compared with the conventional FFT. This is because, the step of
multiplication which occupies a great proportion of operation of
the FFT, is almost eliminated in the processing step of FHT.
Below is concretely illustrated the relation between the FHT
analyzer 16 and the band average frequency analyzer 17. FIG. 4 is a
diagram showing vibration amplitude characteristics of an event, in
which the abacessa represents the time t and the ordinate
represents the vibration amplitude X. FIG. 4 deals with eight
samples X.sub.0, X.sub.1, -X.sub.7 with respect to eight sampling
times t.sub.0, t.sub.1,-t.sub.7. The vibration amplitudes of eight
samples are taken in through the sample-holding circuit 13 and are
converted into digital signals through the A/D converter 14. FIG. 5
is a diagram showing relations in detail among the A/D converter
14, the FHT analyzer 16 and the band average frequency analyzer 17.
The band average frequency analyzer 17 consists of a linear
converter 70, a memory 71, multipliers M and adders add.
In FIG. 5, symbol add designates an adder, and sub a subtractor.
Symbol + of the subtractors means that a signal of the signal line
is subtracted. Symbol X designated at M represents a multiplier.
FIG. 6 shows detailed construction of the FHT analyzer 16. The
vibration amplitude X subjected to the analog-to-digital conversion
is stored in a memory (not shown), and then the operation of an
element u is performed. The operation of the element u is carried
out in accordance with the following equation (10). ##EQU4##
Based on u found according to the equation (10), the element u' is
then operated. The operation of the element u' is carried out in
accordance with the following equation (11). ##EQU5##
By repeating the abovementioned operations n times (n=log.sub.2 N,
where N is a number of the samples), the sequency coefficients
A(0), A(1),-A(7) (general formula, A(k)) can be found. In FIG. 6,
symbol add represents adders and sub subtractors.
Transform coefficients are utilized to transform the outputs A(0),
A(1),-A(7) of the FHT analyzer 16 of FIG. 6 into Fourier
coefficients a.sub.0, a.sub.1, b.sub.1,-b.sub.4.
Examples of the transform coefficients are shown in Table 2.
TABLE 2 ______________________________________ a.sub.0 a.sub.1
a.sub.2 a.sub.3 a.sub.4 ______________________________________
A.sub.0 1.0 A.sub.2 1.306563 -0.541197 A.sub.4 1.414213 A.sub.6
0.541196 1.306562 ______________________________________ b.sub.0
b.sub.1 b.sub.2 b.sub.3 b.sub.4
______________________________________ A.sub.1 1.306563 0.541197
A.sub.3 1.414215 A.sub.5 -0.541195 1.306563 A.sub.7 1.0
______________________________________
The following equation (12) can be obtained if Fourier coefficients
a, b are found using the above transform coefficients. ##EQU6##
In the equation (12), symbol a.sub.0 represents a d-c component,
symbols a.sub.1, a.sub.2, a.sub.3 and a.sub.4 represent sine wave
components, and b.sub.1, b.sub.2, b.sub.3 and b.sub.4 denote cosine
wave components. Referring to Table 2 again, the values remain
practically the same even if numerical figures smaller than the
fifth decimal point are rounded off. As a result, the transform
coefficients employed for the equation (12) are the following five
values: 1.3066, 0.5412, 1.4142, and 1.3066. Therefore, the above
five transform coefficients are stored, and the Fourier
coefficients a and b are found by utilizing the equation (12).
According to the present invention made up of a combination of the
conventional FHT and the linear transform, the individual Fourier
coefficients are not found from the sequency coefficients in
accordance with the equation (12), but the Fourier coefficients are
found as average values of frequency bands. An embodiment of the
present invention therefore is mentioned below with reference to
FIG. 5 again.
D-c components, average value of since waves and average value of
cosine waves are considered below as frequency bands. Since the
transform coefficient is 1, the d-c component a.sub.0 is,
as will be obvious from the foregoing description.
The average value a of the sine waves is, ##EQU7## The average
value b of the cosine waves is, ##EQU8## where,
To the equations (14) and (15), only the following three data are
needed; i.e., 1.8478, 0.7654, and 1.4142. The above three data
serve as transform coefficients for the band averages.
In the band average frequency converter 17 of FIG. 5 the above
three data are stored in the memory 71. In the linear converter 70,
the multiplication is carried out between the data of the memory 71
and the sequency, followed by the addition, and then the operations
are performed according to equations (14) and (15) to find the
average values a and b. According to the abovementioned embodiment,
the average frequency spectrum can be detected which requires a
small memory capacity.
Although the abovementioned average values are related to the sine
and cosine components, the same holds true for the average values
of various harmonics components. As the number of samples N
increase, the band averages can be found maintaining higher
precision. In general, the numbers N=256, 512, 1024,--can be
practically employed.
The general formula (when the number of samples is N) for
transforming the sequency coefficient A into a Fourier coefficient
a which indicates the frequency components, is given by the
following equation (17) ##EQU9## where R represents the components
of running speed, and Rc a specific frequency.
Further, in order to convert the coefficient into a frequency
spectrum, the operation is carried out according to the equation
(18).
For example, a halved running speed P.sub.1/2R is given by
##EQU10##
According to the aforementioned embodiment, the frequency
characteristics can be found in the form of a band with respect to
the causes of vibration shown in Table 1. It is therefore allowed
to properly grasp the causes of vibration and take a necessary
measure.
The object of the present invention can also be accomplished by
using a computer. FIG. 7 shows a flow chart for this purpose.
First, the timeseries signals X.sup.T =[X.sub.0,
X.sub.2,---X.sub.N-1 ] are introduced through a flow 501. Then, a
sequency coefficient A is found in accordance with ##EQU11## in a
flow 502. Based on an average transform coefficient K, the band
average Fourier coefficient a.sub.p =K.sub.p .multidot.A is found.
This processing is the same as the processing of the aforementioned
embodiment. Checking is then effected. That is, whether the band
Fourier coefficient a in a flow 504 is within an allowable value
L.sub.p (abnormality discrimination level) is checked. When the
requirement has been satisfied, the operation is shifted to a flow
506 where the checking is effected as to whether all of the samples
have been scanned. When the scanning has been completed, the
operation is shifted to a flow 507. When all of the procedures have
been completed, the operation is ready for the next samples. When
the flow 504 has not been satisfied, the state at that moment is
indicated by means of the flow 505. The checking in the
abovementioned steps can also be applied to the case of FIG. 5.
Below is mentioned another embodiment of the present invention.
FIG. 8 shows the embodiment in which the aforementioned
conventional FHT and the linear transform are combined together.
Therefore, the converter section 17 has been so constructed as to
perform the operation of equation (12). The greatest feature of
this embodiment is the provision of a comparator section 19 between
the analyzer 16 and the analyzer 17. The comparator section 19 has
comparators of a number corresponding to the number of sequency
coefficients. The individual comparators introduce the
corresponding sequency coefficients and allowable values As which
have been preset for each of the sequency coefficients, and compare
the two. The allowable value As of the sequency coefficient serves
as a reference value by which it can be so determined that the
values in excess of the reference value As are indicative of the
abnormal conditions. The comparators (As.sub.0 to As.sub.7 in this
case) compare the sequency coefficients Ak with reference to the
allowable values Ask. The comparators do not produce the output
when the difference from the allowable values is smaller than a
predetermined width Mp, and produce the sequency coefficient Ak
when the difference is greater than the width Mp to indicate that
the machine is under abnormal conditions. By utilizing the sequency
coefficient determined as indicative of the abnormal conditions,
the analyzer 17 finds a related Fourier coefficient. Based on the
results of the Fourier coefficient, the checking is effected again
as to whether the machines are under normal or abnormal conditions.
Namely, in the aforementioned embodiment, the primary abnormality
checking is effected in regard to the sequency coefficient. When it
is checked that the machines are under abnormal conditions, a
Fourier coefficient is found to effect the secondary abnormality
checking. In case only one sequency coefficient is determined to be
defective, it becomes necessary to calculate other sequency
coefficients (except a.sub.0) to find a Fourier coefficient. It is
therefore necesssary to find the Fourier coefficient by taking the
above sequency coefficients into consideration. Although not
diagramed, the results of the individual comparators are checked by
a control circuit as to whether or not the comparators should
produce the outputs.
FIG. 9 is a flow chart of the present invention when it is
constructed by the use of a computer. The deviation between the
allowable value Ask and each of the sequency coefficients Ak is
found in a block 508. Then the checking is effected in a block 509
as to whether the deviation .epsilon. is smaller than the value Mp.
When the deviation is smaller than Mp, the operation is shifted to
a block 506, and when the deviation is greater than Mp, the
operation is shifted to a block 510 to find a Fourier coefficient.
The display is then made by a block 511. These embodiments can also
be applied to the case of band average. In this case, also, the
comparator section 19 is provided between the analyzer 16 and the
analyzer 17.
In the foregoing was mentioned mainly in regard to the processing
of the detected vibration signals. Below is mentioned the control
of operation of a turbine and a generator based on the diagnosed
results of these processed signals.
FIG. 10 is a block diagram showing the whole setup, in which a
high-pressure turbine HP designated at 51, an intermediate-pressure
turbine IP, a low-pressure turbine LP designated at 52, and a
generator G designated at 53 are directly coupled together.
Reference numeral 39 denotes a running speed detector, and
reference numerals 40 to 45 denote vibration amplitude detectors
mounted on the bearings. Reference numeral 48 represents a
vibration diagnosing device which diagnoses the rotary machines
based on the vibration amplitude signals, 47 a demand set device
which corrects the schedule signals from a turbine start-up
scheduler 46 for controlling the speed relying upon the results of
diagnosis of the vibration signals (signals detected by the
detectors 40 to 45) from rotary members, and reference numeral 55
designates a turbine speed regulator which controls the speed of
the turbine responsive to the signals set by the demand set device
47. Symbol M represents a motor for operating a valve MSV-SV 64,
MSV-SV a supplemental valve of a main stop valve, MSV a main stop
valve, and CV a control valve.
The turbine speed regulator controls a main steam-blocking by-pass
valve 64 responsive to the deviation between a signal 203 from the
running speed detector 39 and a signal from the demand set device
47, and controls the flow rate of the steam to the turbine 51 such
that a desired running speed is attained. Although it was mentioned
that the signals from the turbine start-up scheduler are corrected
relying upon the diagnosed results, it may otherwise be mentioned
in a way that the signals are set prior to the schedule signals to
control the speed of the turbine.
FIG. 11 is a diagram showing a concrete setup of a vibration
diagnosing device 48, in which reference numerals 216 and 217
denote band filters, 218 a multiplexer, 219 a sample holder, 220 an
A/D converter, 221 a timing generator circuit which generates the
timing is synchronism with the running speed, 222 a Fourier
transformer, 223 a discriminator for discriminating the state of a
rotary member based on the Fourier-transformed signals, and a
diagnosis device 224 is made up of the Fourier transformer 222 and
the discriminator 223.
Reference numeral 204 represents an analog signal of shaft
vibration, 205 a digital signal of shaft vibration, 206 a harmonics
spectrum signal, and reference numeral 207 denotes a demand set
signal based on the analysed results which will be fed to the
demand set device 47. A signal source 208 works to switch the
multiplexer. That is, the multiplexer is switched by the signals of
the signal source 208, so that a plurality of vibration detecting
signals are successively switched and introduced.
FIG. 12 shows an example of a waveform, in which diagram (a) shows
the waveform of a shaft vibration signal detected by the vibration
detector, for example, the waveform of a signal 201 of FIG. 11.
Diagram (b) shows a signal after it has passed through a band
filter, from which it will be recognized that harmonics components
have been removed. A signal 204 of FIG. 11 just corresponds to this
signal.
Diagram (c) shows an output signal of the sample holding circuit. A
signal 204' of FIG. 11 corresponds to this signal. Diagram (d)
shows digital signals of shaft vibration converted through the A/D
converter. A signal 205 of FIG. 11 is corresponding to this signal.
In the diagram (d), the signal has been converted into a digital
signal consisting of 11 bits (MSD, however, is a sign bit) with
respect to the output signal 204' of the sample holding
circuit.
As mentioned already, in the case of the FHT, these time series
digital signals will be fed to the samples X.sub.0 X.sub.1,
X.sub.2,---X.sub.7 of FIG. 6, so that the element u is operated to
find the sequency coefficients A(0), A(1), A(2),---A(7). To
transform them into Fourier coefficients a.sub.0, a.sub.2,
b.sub.1,---b.sub.4, the transform coefficients shown in Table 2
will be used. Here, for the purpose of simplicity, although the
number of samples is N=8 (X.sub.0, X.sub.1, X.sub.2,---X.sub.7),
the number of samples will be practically expanded to 256, 512,
1024 or greater as mentioned earlier.
Diagram (a) of FIG. 13 shows the state of vibration amplitudes at
the time of starting the trubogenerator. There exist several
critical speed regions where the vibration amplitude increases
before a rated running speed is reached. Usually, the first
critical speed region lies near 1000 rpm, the second critical speed
region lies in the vicinity of 2000 rpm, and the third, fourth and
fifth critical speed regions develop from about 3000 to 3400
rpm.
Diagram (b) of FIG. 13 shows a general speed-raising pattern during
the starting period, in which symbols A to D are corresponding to A
to D of the diagram (a). According to the present invention, the
frequencies of vibration signals are analysed in these sheltered
speed regions to diagnose the condition of the torbogenerator based
on the specturm analysis of all frequencies, or to diagnose the
conditions of particular frequency components having predetermined
relation to the running speeds as shown in Table 1, thereby to
control the operation.
FIG. 14 shows the case in which the diagnosis is carried out by
setting threshold values. The abscissa represents the component of
running speed indicated in terms of a ratio dB with respect to the
vibration amplitude 100 microns (peak to peak), or in terms of a
ratio dB with respect to the over-all frequency components, or in
terms of an absolute value, or in various other forms. The
ordinate, in this case, represents a frequency component of 1/2
running speed. Like the case of the abscissa, the quantity will be
indicated in terms of a ratio dB or in terms of an absolute
value.
Referring to FIG. 14, symbol U represents a speed-raising region
where the running speed is accelerated, H a holding region where
the running speed is held constant, D a region where the machine is
operated at a lower sheltered speed, and symbol T represents a trip
region where the operation is stopped. That is, in the region U,
the running speed will be accelerated according to the start-up
schedule (or speed-raising schedule) shown in the diagram (b) of
FIG. 13. The start-up schecule signal is produced, for example, by
the turbine start-up scheduler 46 of FIG. 10.
In the region H, the operation is carried out for a predetermined
period of time maintaining a predetermined speed. When the running
speed is still in the region H even after the predetermined period
of time has passed, the operation is performed by lowering the
running speed to a lower sheltered speed. Here, if it is supposed
that the machine is operating in the region C in the diagram (a) of
FIG. 13, the operation in the lower sheltered region means that the
operation is carried out in the speed region B. This means that
even if the running speed is in the region H, the operation is
carried out at a reduced speed just like in the region D after the
operation has been performed for a predetermined period of time
maintaining the constant speed.
With reference to the region D, when the operation performed in the
region C of FIG. 13 reached the region D of FIG. 14, the operation
thereafter is carried out by lowering the speed to the region B of
FIG. 13.
FIG. 14 shows the relation between the components of the running
speed and the components of the halved running speed. Even if the
components of the halved running speed are small, the increase in
the components of the running speed may lead the operation to the
tripping region. The reason is because, as will be obvious from
Table 1, the cause of vibration different from the misalignment of
bearings may have been developed, for example, thermal bending
caused by rubbing may have been developed. FIG. 14 shows a relation
between the components of the running speed and the components of
the halved running speed. Here, by monitoring the components of the
1/3 running speed, components or critical speed, and components of
the doubled running speed, it is possible to monitor and diagnose
the causes of vibration.
To summarize the foregoing, below is mentioned with reference to
flow diagrams of FIG. 15 the method of controlling the operation
while diagnosing abnormal conditions according to the present
invention.
A step 301 for processing the input introduces the running speed
(rpm) of the turbine and generator as well as shaft vibration
signals X measured at each point of the bearings [(number of
samples N).times.(number of channels)]. A step 302 for extracting
the initial symptoms finds the sequency coefficiencies A(0) to
A(N-1) according to the equation (6). A step 303 for discriminating
abnormal conditions finds a sequency spectrum .vertline.A.vertline.
in accordance with the equation (20), detects a deviation with
respect to a sequency spectrum .vertline.A normal.vertline. of
operation under normal condition, and discriminates whether the
deviation is great or small with respect to a predetermined small
value L.
If,
.vertline.A.vertline.-.vertline.A normal.vertline..sqroot.L
the steps 304 to 307 discriminate in which speed region among the
resions A to B of FIG. 13 the turbine is running. Symbols A to D
represent predetermined speed regions avoiding such regions that
contain first, second, third, fourth and fifth critical speeds.
Patterns I to IV corresponding to each of the speed regions are
selected by means of steps 308 to 311.
An example of the pattern II is shown in the diagram (C) of FIG.
15. The pattern III is the same as the pattern II in regard to its
abscissa and ordinate, but has different setpoint levels U, H, D
and T. The pattern I shows the case in which the ordinate is 1/2 R
and 1/3 R as shown in the diagram D of FIG. 15. In the case of the
pattern I, the running speed is smaller than the first critical
speed, and hence Rc may be neglected.
The pattern IV has a component 2R in addition to those of the
patterns II and III of the diagram (C) of FIG. 15.
If now the turbine is running at a speed which pertains to the
region B of FIG. 13, the pattern II is selected (step 309). In the
next step 316 (diagram B of FIG. 15), the WFT processing is
performed in accordance with the equation (17) to transform the
sequency coefficient into a Fourier coefficient a a which indicates
frequency components. As will be obvious from the diagram C of FIG.
15, the ordinate in this case represents 1/2 R, 1/3 R and Rc.
Therefore, only the corresponding portions need be selected and
operated in accordance with the equation (17). For example, the
elements a.sub.0, b1/3R, a1/3R, b1/2R, a1/2R, b.sub.Rc and a.sub.Rc
should be operated. Further, as for the components of rotating
frequencies represented by the ordinate of the diagram C of FIG.
15, the elements corresponding to b.sub.R and a.sub.R should be
operated in accordance with the equation (17).
The subsequent steps 317 to 320 discriminate to which region among
the operation patterns U, H, D and T of the diagram C of FIG. 15,
the vibration signals pertain. In other words, the steps 317 to 320
discriminate in regard to 1/2R, Rc and 1/3R in the case of the
pattern II. The corresponding speeds are than controlled (steps 321
to 324). Concretely speaking, the discriminated result is given as
a setpoint value to the turbine speed regulator 55 prior to the
start-up schedule signal which has been preset by the demand set
device 47 of FIG. 10. The level of priority has a relation
T>D>H>U, and the operation is performed based on a pattern
having the highest level among the selected ones.
The step 313 displays the vibration spectrum (for example, by means
of a cathode-ray tube), and the step 314 discriminates whether the
processing has been performed for all channels. If the processing
has not been effected for all channels, other channels are selected
(step 315) to repeat the same processing. Here, the word "channels"
represents vibration detectors 39 to 45 of FIG. 10.
Although the foregoing description has dealt with the case of
operating the predetermined frequency components, such as frequency
components of 1/2R, the frequency components in the vicinity of the
abovesaid components may also be operated to find average spectra.
In that case, b(1/2R+1), b(1/2R-1), b(1/2R) and a(1/2R+1),
a(1/2R-1), a(1/2R) should be calculated in accordance with the
equation (17). An average value may also be found in regard to a
predetermined region in the vicinity of particular frequency
components. For instance, a calculation 1/2R.+-.r may be carried
out in regard to a predetermined frequency region r with 1/2R as a
reference. That is, in the case of the equation (17), the
calculation is carried out in regard to b(1/2R.+-.r) and
a(1/2R.+-.r). Referring to Table 1, i=29, 30, 31 when p=1 are
examples in the case of 1/2R.+-.1. Here, since m.sub.1 =6 has been
selected, it is allowed to calculate the case 1/4R.+-.1, i.e., to
calculate the cases i=14, 15 and 16.
To diagnose the conditions of a rotary machine based on the average
frequency components in the vicinity of the preselected frequencies
or including given regions in the vicinity of the preselected
frequencies, is advantageous in regard to that erroneous diagnosis
caused by noise signals from the vibration detectors can be
avoided, and the deviation in sampling phases can be compensated.
In the case of the pattern II, this can be represented as shown in
the diagram E of FIG. 15.
In the step 303 of the diagram A of FIG. 15, the deviation is
detected with respect to .vertline.A normal.vertline. in order to
absorb dispersion caused by the rotary machines.
Diagrams (a) to (d) of FIG. 16 show one of the effects of the
present invention.
Referring to the diagram (a), let it be supposed that the vibration
amplitude signal at the present running speed is as shown in the
diagram (b). The waveforms are smaller than the vibration
amplitude. Therefore, no abnormal condition is detected with the
conventional average value system. The vibration then gives rise to
the occurrence of oil whirl phenomenon which produces vibration of
excessive amplitude. On the other hand, if the frequencies are
analysed and the spectrum is monitored as done by the present
invention, it is possible to detect the symptom of oil whirl at a
point a . Referring to the diagram (d), spectra indicated by black
circles indicate such symptoms. It will be recognized that the test
machine has a specific vibration frequency of 22.5 Hz, and the
spectrum at this frequency is particularly greater than those of
other frequencies. This indicates that there is a symptom of oil
whirl.
According to the present invention, therefore, even when the
vibration amplitude is small or even when the average value of the
vibration amplitude is small, it is possible to foresee the
development of any abnormal vibrations. It is therefore possible to
detect abnormal vibrations in an early time to safely control the
operation.
The ordinate of the diagram (d) of FIG. 16 represents frequency
spectra normalized by peak-to-peak value of vibration
waveforms.
FIG. 17 shows the case when the operation is started by applying
the method of the present invention in comparison with the case
when the operation is started according to the conventional art. A
solid line represents the case to which is applied the present
invention. According to the present invention, if abnormal
condition is detected at a point a , the running speed is once
decreased to a low-speed sheltered region, and the running speed is
accelerated again to a rated running speed. According to the
conventional art (broken line), on the other hand, the detection of
abnormal condition is delayed as indicated by a point b .
Consequently, the average value of vibration amplitudes plunges
into the tripping region such that the operation is tripped. The
operation therefore must be started again after the cause of
abnormal condition has been clarified. Thus, the present invention
is capable of detecting abnormal conditions in an early time,
making it possible to avoid unnecessary tripping.
Furthermore, a deviation e between the measured sequency spectrum a
and the standard value as may be compared with a predetermined
allowable value to discriminate abnormal condition. These relations
are given by equations (20) to (22). ##EQU12##
Rotary members such as turbines and generators contain residual
unbalance to some extent introduced during the steps manufacturing
and installation. When the rotary members are rotated, therefore,
the residual unbalance produces exciting force which creates
vibration of shaft with the components of running speed as centers
even under normal conditions. Therefore, during the initial stage
of acceleration, it is difficult to detect the development of
abnormal condition even when it is developed because the vibration
components under the normal condition work as disturbance. To
detect abnormal characteristics maintaining high degree of
sensitivity, therefore, the vibration characteristics under normal
condition should be stored beforehand, and the deviation therefrom
should be monitored. With the monitoring in the conventional time
regions, however, it is difficult to bring the stored vibration
waveforms under normal condition into phase with the vibration
waveforms measured each time.
According to this embodiment, however, the waveforms are
transformed into sequency coefficients and compared with the
characteristics under normal condition, whereby the effects of
phase need not be taken into consideration.
The foregoing embodiment of the present invention has dealt with
the case of analyzing the frequencies by means of digital signals.
The frequencies, however, may be analyzed based on analog signals.
In that case, however, it is necessary to employ an analog filter
which is capable of automatically changing the time constant
responsive to the running speed of the rotary machines. It is
because the frequency components must be analysed with reference to
the frequencies related to the rotating frequency as shown, for
example, in the diagram C of FIG. 15. However, the filter for
specific vibration frequency determined from the characteristics of
the rotary machine, may have a fixed time constant.
When abnormal conditions under rated running speed are to be
diagnosed, filters having time constants determined for their
respective requirements may be employed.
* * * * *